YES
TRS:
 {f(f(a(), x), y) -> f(y, f(x, f(a(), f(h(a()), a()))))}
 DP:
  Strict:
   {f#(f(a(), x), y) -> f#(y, f(x, f(a(), f(h(a()), a())))),
    f#(f(a(), x), y) -> f#(x, f(a(), f(h(a()), a()))),
    f#(f(a(), x), y) -> f#(a(), f(h(a()), a())),
    f#(f(a(), x), y) -> f#(h(a()), a())}
  Weak:
  {f(f(a(), x), y) -> f(y, f(x, f(a(), f(h(a()), a()))))}
  EDG:
   {(f#(f(a(), x), y) -> f#(x, f(a(), f(h(a()), a()))), f#(f(a(), x), y) -> f#(h(a()), a()))
    (f#(f(a(), x), y) -> f#(x, f(a(), f(h(a()), a()))), f#(f(a(), x), y) -> f#(a(), f(h(a()), a())))
    (f#(f(a(), x), y) -> f#(x, f(a(), f(h(a()), a()))), f#(f(a(), x), y) -> f#(x, f(a(), f(h(a()), a()))))
    (f#(f(a(), x), y) -> f#(x, f(a(), f(h(a()), a()))), f#(f(a(), x), y) -> f#(y, f(x, f(a(), f(h(a()), a())))))
    (f#(f(a(), x), y) -> f#(y, f(x, f(a(), f(h(a()), a())))), f#(f(a(), x), y) -> f#(y, f(x, f(a(), f(h(a()), a())))))
    (f#(f(a(), x), y) -> f#(y, f(x, f(a(), f(h(a()), a())))), f#(f(a(), x), y) -> f#(x, f(a(), f(h(a()), a()))))
    (f#(f(a(), x), y) -> f#(y, f(x, f(a(), f(h(a()), a())))), f#(f(a(), x), y) -> f#(a(), f(h(a()), a())))
    (f#(f(a(), x), y) -> f#(y, f(x, f(a(), f(h(a()), a())))), f#(f(a(), x), y) -> f#(h(a()), a()))}
   SCCS:
    Scc:
     {f#(f(a(), x), y) -> f#(y, f(x, f(a(), f(h(a()), a())))),
      f#(f(a(), x), y) -> f#(x, f(a(), f(h(a()), a())))}
    SCC:
     Strict:
      {f#(f(a(), x), y) -> f#(y, f(x, f(a(), f(h(a()), a())))),
       f#(f(a(), x), y) -> f#(x, f(a(), f(h(a()), a())))}
     Weak:
     {f(f(a(), x), y) -> f(y, f(x, f(a(), f(h(a()), a()))))}
     UR:
      {f(f(a(), x), y) -> f(y, f(x, f(a(), f(h(a()), a()))))}
      BOUND:
       Bound: match(-raise)-DP-bounded by 2
       Automaton:
        {     h_2(20) -> 21*
              h_1(15) -> 16*
              h_0(14) -> 10*
              h_0(13) -> 10*
              h_0(12) -> 11*
              h_0(11) -> 10*
              h_0(10) -> 10*
               h_0(9) -> 10*
                a_2() -> 20*
                a_1() -> 15*
                a_0() -> 12*
         f#_2(17, 23) -> 5*
         f#_1(24, 25) -> 5*
         f#_1(24, 24) -> 5*
         f#_1(19, 24) -> 5*
         f#_1(18, 24) -> 5*
         f#_1(18, 19) -> 5*
         f#_1(18, 18) -> 5*
         f#_1(14, 18) -> 5*
         f#_1(13, 18) -> 5*
         f#_1(12, 18) -> 5*
         f#_1(11, 18) -> 5*
         f#_1(10, 18) -> 5*
          f#_1(9, 18) -> 5*
         f#_0(14, 14) -> 5*
          f#_0(14, 9) -> 5*
         f#_0(13, 14) -> 5*
         f#_0(12, 14) -> 5*
         f#_0(11, 14) -> 5*
         f#_0(10, 14) -> 5*
          f#_0(9, 14) -> 5*
           f#_0(9, 9) -> 5*
          f_2(21, 20) -> 22*
          f_2(20, 22) -> 23*
          f_1(24, 25) -> 19*
          f_1(24, 24) -> 25*
          f_1(19, 24) -> 19*
          f_1(18, 24) -> 25*
          f_1(18, 19) -> 19*
          f_1(18, 18) -> 25*
          f_1(17, 18) -> 24*
          f_1(16, 15) -> 17*
          f_1(15, 17) -> 18*
          f_1(14, 18) -> 19*
          f_1(13, 18) -> 19*
          f_1(12, 18) -> 19*
          f_1(11, 18) -> 19*
          f_1(10, 18) -> 19*
           f_1(9, 18) -> 19*
          f_0(14, 14) -> 9*
          f_0(14, 13) -> 9*
          f_0(14, 12) -> 9*
          f_0(14, 11) -> 9*
          f_0(14, 10) -> 9*
           f_0(14, 9) -> 9*
          f_0(13, 14) -> 9*
          f_0(13, 13) -> 9*
          f_0(13, 12) -> 9*
          f_0(13, 11) -> 9*
          f_0(13, 10) -> 9*
           f_0(13, 9) -> 9*
          f_0(12, 14) -> 9*
          f_0(12, 13) -> 14*
          f_0(12, 12) -> 9*
          f_0(12, 11) -> 9*
          f_0(12, 10) -> 9*
           f_0(12, 9) -> 9*
          f_0(11, 14) -> 9*
          f_0(11, 13) -> 9*
          f_0(11, 12) -> 13*
          f_0(11, 11) -> 9*
          f_0(11, 10) -> 9*
           f_0(11, 9) -> 9*
          f_0(10, 14) -> 9*
          f_0(10, 13) -> 9*
          f_0(10, 12) -> 9*
          f_0(10, 11) -> 9*
          f_0(10, 10) -> 9*
           f_0(10, 9) -> 9*
           f_0(9, 14) -> 9*
           f_0(9, 13) -> 9*
           f_0(9, 12) -> 9*
           f_0(9, 11) -> 9*
           f_0(9, 10) -> 9*
            f_0(9, 9) -> 9*}
       Strict:
        {f#(f(a(), x), y) -> f#(y, f(x, f(a(), f(h(a()), a()))))}
       EDG:
        {(f#(f(a(), x), y) -> f#(y, f(x, f(a(), f(h(a()), a())))), f#(f(a(), x), y) -> f#(y, f(x, f(a(), f(h(a()), a())))))}
        SCCS:
         Scc:
          {f#(f(a(), x), y) -> f#(y, f(x, f(a(), f(h(a()), a()))))}
         SCC:
          Strict:
           {f#(f(a(), x), y) -> f#(y, f(x, f(a(), f(h(a()), a()))))}
          Weak:
          {f(f(a(), x), y) -> f(y, f(x, f(a(), f(h(a()), a()))))}
          UR:
           {f(f(a(), x), y) -> f(y, f(x, f(a(), f(h(a()), a()))))}
           BOUND:
            Bound: match(-raise)-DP-bounded by 1
            Automaton:
             {     h_1(17) -> 18*
                   h_0(16) -> 11*
                   h_0(15) -> 11*
                   h_0(14) -> 11*
                   h_0(13) -> 12*
                   h_0(12) -> 11*
                   h_0(11) -> 11*
                   h_0(10) -> 11*
                     a_1() -> 17*
                     a_0() -> 13*
              f#_1(21, 21) -> 5*
              f#_1(16, 21) -> 5*
              f#_0(16, 16) -> 5*
              f#_0(15, 16) -> 5*
              f#_0(14, 16) -> 5*
              f#_0(13, 16) -> 5*
              f#_0(12, 16) -> 5*
              f#_0(11, 16) -> 5*
              f#_0(10, 16) -> 5*
               f_1(21, 21) -> 21*
               f_1(20, 21) -> 21*
               f_1(20, 20) -> 21*
               f_1(19, 20) -> 21*
               f_1(18, 17) -> 19*
               f_1(17, 19) -> 20*
               f_1(16, 20) -> 21*
               f_1(15, 20) -> 21*
               f_1(14, 20) -> 21*
               f_1(13, 20) -> 21*
               f_1(12, 20) -> 21*
               f_1(11, 20) -> 21*
               f_1(10, 20) -> 21*
               f_0(16, 16) -> 16 | 10
               f_0(16, 15) -> 16*
               f_0(16, 14) -> 10*
               f_0(16, 13) -> 10*
               f_0(16, 12) -> 10*
               f_0(16, 11) -> 10*
               f_0(16, 10) -> 10*
               f_0(15, 16) -> 16 | 10
               f_0(15, 15) -> 16*
               f_0(15, 14) -> 10*
               f_0(15, 13) -> 10*
               f_0(15, 12) -> 10*
               f_0(15, 11) -> 10*
               f_0(15, 10) -> 10*
               f_0(14, 16) -> 10*
               f_0(14, 15) -> 16*
               f_0(14, 14) -> 10*
               f_0(14, 13) -> 10*
               f_0(14, 12) -> 10*
               f_0(14, 11) -> 10*
               f_0(14, 10) -> 10*
               f_0(13, 16) -> 10*
               f_0(13, 15) -> 16*
               f_0(13, 14) -> 15*
               f_0(13, 13) -> 10*
               f_0(13, 12) -> 10*
               f_0(13, 11) -> 10*
               f_0(13, 10) -> 10*
               f_0(12, 16) -> 10*
               f_0(12, 15) -> 16*
               f_0(12, 14) -> 10*
               f_0(12, 13) -> 14*
               f_0(12, 12) -> 10*
               f_0(12, 11) -> 10*
               f_0(12, 10) -> 10*
               f_0(11, 16) -> 10*
               f_0(11, 15) -> 16*
               f_0(11, 14) -> 10*
               f_0(11, 13) -> 10*
               f_0(11, 12) -> 10*
               f_0(11, 11) -> 10*
               f_0(11, 10) -> 10*
               f_0(10, 16) -> 10*
               f_0(10, 15) -> 16*
               f_0(10, 14) -> 10*
               f_0(10, 13) -> 10*
               f_0(10, 12) -> 10*
               f_0(10, 11) -> 10*
               f_0(10, 10) -> 10*}
            Strict:
             {}
            Qed